Defining Tuning and Intonation 
A musical system can have only one state of system that is determined by a fundamental frequency of vibration. The fundamental tone is the lowest possible mode of vibration that can exist in the system, and every overtone is determined as a simple harmonic multiple of the fundamental frequency of vibration. Intonation is the process of correctly adjusting the specific pitch of the fundamental frequency of vibration according to a tuning rule. In contrast, tuning and temperament are pitch-independent functions that can be sounded at any level. In polyphonic music the union of musical instruments in any key is possible because every instrument and voice shares a common fundamental, scale, and temperament. When multiple primary oscillators can be individually intonated in a way that makes a polyphonic union possible we commonly say the instruments are “in tune.” Tuning is a word often used in a general, confusing way to mean either intonation or temperament, but more importantly, the specific meaning of the word “tuning” is the pitch-independent interval between 2 or more strings. This is the meaning of “guitar tuning”: a set of intervals between strings that can be intonated at any desired pitch by controlling string gauge, length, and tension. For example the commonly-used guitar tunings Open G and Open A (intervals from low to high 5 7 5 4 3) are exactly the same tuning but intonated at a system fundamental of D2 and E2 respectively. The so called “Standard” tuning for guitar E A D G B E is 5 5 5 4 5. A capo changes intonation by shortening string length but does not change tuning. When a single tuning note is altered the guitarist must re-learn every chord and scale, and this effect is most dramatic when inner strings are altered.
Musical staff is read accord of key signature; tablature is read according to tuning. Both staff and tabs can be intonated at any level but are usually expressed at concert pitch. The guitar however is actually intonated by adjusting the tuning relative to the lowest note. The distinction between tuning and intonation is critical to guitar because the shape of chords and scales on guitar is determined by tuning and not by intonation.
When two more strings are joined under the same rules (that is the same fret system), the system fundamental no longer determines the state of system uniquely but is instead the system fundamental K1 is effectively replaced by a new system fundamental: the interval between the strings K2 and K2.
The interesting aspect of tunings is while thousands of guitar tunings are in theory possible, only about 30 guitar tunings are in common use and only slight greater than 100 guitar tunings have ever been reported to have any useful harmonic expression. The vast majority of popular music relies on about half a dozen tunings. There is no “Standard” guitar tuning, any more than a standard language exists in English, and in that sense the concept of altered tuning is misleading. Tunings are important culturally because while every guitar tuning could be made with the same set of notes, the expression of music on guitar is determined by the tuning just as this sentence is determined by English and not the alphabet. This means that the listener, who cannot see the guitar, cannot know how the guitar is actually played and is unaware of the guitar tuning that is used.
The fundamental in a musical system, once lost cannot be recovered, but the tuning can be discovered given enough information about the system. Recognizing the guitar tuning system by ear is difficult at best, and impossible without training.
Interval, melody, and harmony 
The lower or upper pitch of an interval may be sharp or flat, or both pitches of an interval may be out of tune.
If the lower pitch is sharp or the upper pitch is flat, the interval may be said to be flat given that as a whole it is too narrow; while if the lower pitch is flat or the upper pitch is sharp, the interval may be said to be sharp given that as a whole it is too wide. Intervals are conventionally measured from the bottom, as such in an interval that is too wide the upper pitch is thus sharp. For example, the "flat fifth" of meantone temperament.
However, the interval itself may be in tune, in relation to itself (i.e. both notes of the interval are in tune in relation to each other), but flat or sharp as a whole and thus both notes of the interval is out of tune.
A melody or harmony is flat or sharp if it is too high or low, respectively. A melody may be successively both sharp and flat.[clarification needed] A harmony may be simultaneously and successively both sharp and flat.[clarification needed]
With fretless string instruments such as cellos, intonation depends on the musician pressing with his fingers at the exact spot on the instrument's fingerboard.
Fretted instrument intonation 
Several factors affect fretted instrument intonation, including depth of the string slots in the nut, bridge saddle position, and the position of the frets themselves.
On fretted string instruments, pushing a string against a fret—aside from raising the string's pitch because it shortens the string—also causes a slight secondary raise in pitch because pushing the string increases its tension. If the instrument doesn't compensate for this with a slight increase in the distance from the bridge saddle to the fret, the note sounds sharp.
Most electric fretted string instruments have individually adjustable bridge saddles, adjustable with a screw driver or Allen wrench. Acoustic fretted instruments typically have either a floating bridge, held in place by string tension, or a fixed bridge, such as a pin bridge on an acoustic guitar. A luthier or technician adjusts a floating bridge simply by carefully changing its position until the intonation is correct. Adjusting intonation on a fixed bridge involves carefully shaping the bridge saddle with a file to alter the string's contact point.
Another cause of poor intonation on a fretted instrument is that the maker didn't cut the string slots in the nut deep enough. If the string is higher than fret height at the nut, the string deflection-caused pitch increase is progressively greater closer to the nut.
Other instruments 
Like unfretted string instruments, the tenor trombone relies on the musician precisely positioning something, in this case the trombone's slide. The slide's pitch adjustment on a single partial is approximately the interval of a tritone on a slide length of over 80 centimeters.
Intonation sensitivity 
Intonation sensitivity is "determined by how the preference for a chord varies with the tuning, or mistuning, of the center note," and may be used to assess and evaluate a known or new chord and its perceptibility as the harmonic basis for a scale. For example, the chord formed by pitches in the ratios 3:5:7 has a very similar pattern of intonation sensitivity to the just major chord, formed by 4:5:6—more similar than does the minor chord. The major or minor triad may be used to form the diatonic scale and the 3:5:7 triad may be used to form the Bohlen–Pierce scale.
Semiotic concept 
The semiotic concept came to musicology from linguistics. In Soviet musicology, it refers to Boris Asafiev’s concept of intonation in music. This concept looks at intonation as a basis of musical expression, and relates it to the peculiarities of different national or personal styles. The basis of the intonation doctrine was laid by Russian musicologist Boleslav Yavorsky (1877-1942) and later developed by Asafiev.
- Max V. Mathews and John R. Pierce (1989). "The Bohlen-Pierce Scale", p.165-66. Current Directions in Computer Music Research, Max V. Mathews and John R. Pierce, eds. MIT Press.
- Konrad Schwingenstein: Intonation of stringed instruments with straight frets, http://www.pepithesecond.com
- Malcolm H Brown: The soviet Russian concepts of "intonazia" and "musical imagery", http://mq.oxfordjournals.org/cgi/content/citation/LX/4/557
- Karen Pegley: Censored Musical Messages, http://www.chass.utoronto.ca/epc/srb/srb/censored.html
- N Mahoney: Intonation on the Classical Guitar, http://www.classical-guitars-plus.co.uk/guitar_info/784__Intonation
See also